Despite its potential, wave energy extraction technology is not yet mature due to a few challenges. The Department of Energy reported in 2012 that the world wave installed capacity is less than 5 MW, mostly produced on a pre-commercial basis. See U.S. Department of Energy, “Marine and hydrokinetic technology database,” December, 2012. One of the main challenges is the design of an effective control strategy that enables the harvesting of higher levels of energy. Another challenge is the limitation of the existing theory and practice. Energy harvesting is about the wave energy converter (WEC) motion and control. The fundamental theory that is being used to describe this motion is inherited from ship hydrodynamics. Ships are usually designed so as to not move in the vertical (heave) direction or rotate in the pitch or roll directions. Hence most theories, designs, and control algorithms are based on the assumption of small motion in these directions, which yield the linear dynamic models. WEC devices, however, need to heave and/or pitch in order to harvest energy. Several references have motivated the use of a multiple-degree-of-freedom (MDOF) WEC as opposed to a single DOF WEC. See D. V. Evans, J. Fluid Mech. 77(1), 1 (1976). Evans extended the results of two-dimensional WECs to bodies in channels and accounts for the body orientation on the energy harvesting. D. V. Evans, “Some theoretical aspects of three-dimensional wave energy absorbers.” Proceedings of the first symposium on wave energy utilization, Chalmers University of Technology, Gothenburg, Sweden, pp 77-106, September 1979. In fact, French and Bracewell point out that the power that can be extracted from a mode that is antisymmetric to the wave (such as pitch and surge) is twice as much as can be extracted from a mode that is symmetric (such as heave). See M. J. French and R. H. Bracewell, “P. S. FROG A point-absorber wave energy converter working in a pitch/surge mode,” Proceedings of The Fifth International Conference on Energy Options: the role of alternatives in the world energy scene, University of Reading, Reading, Berkshire, UK, IEE, September 1987. Yavuz recently modeled the pitch-surge motions assuming no heave motion; hence there is no effect from the heave motion on the pitch-surge power conversion. See Hakan Yavuz, Int. J. Green Ener. 8, 555 (2011). The mathematical model used for the motions in these two DOFs is coupled through mass and damping only; there is no coupling in the stiffness. It has been observed, however, that floating structures can be subject to parametric instability arising from variations of the pitch restoring coefficient. See Carlos Villegas and Haite van der Schaaf, “Implementation of a pitch stability control for a wave energy converter,” Proceedings of 10th Euro. Wave and Tidal Energy Conference, Southampton, U K, 2011. Villegas and Haite describe an experimental heaving buoy for which the parametric excitation causes the pitch motion to grow resulting in instability. A harmonic balance approach is implemented to cancel this parametric resonance and results of tank experiments are described.
As described herein, the equations of motion for a 3-DOF WEC have a second order term that causes the heave motion to parametric excite the pitch mode; and the pitch and surge motions are coupled. For relatively large heave motions, which are needed for higher energy harvesting, it is not possible to neglect this parametric excitation term. Rather, the controller of the present invention leverages this nonlinear term for optimum energy harvesting.